Finite Group Databasebeta

← C11×#2720 #13065558

Subgroups — C11×#2720 #13065558

Order 1408.

472 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#125C211yesmaximal, characteristic, complemented
2C2×C11×C22⋊Q8C211yesmaximal, characteristic
3C11×#400C211yesmaximal, characteristic, complemented
4C11×#399C211yesmaximal, characteristic
5C11×#398C211yesmaximal, characteristic, complemented
6C11×#396C211yesmaximal, characteristic
7C11×#395C211yesmaximal, characteristic, complemented
8C11×#395C211yesmaximal, characteristic, complemented
9C11×#389C211yesmaximal, characteristic, complemented
10C11×#388C211yesmaximal, characteristic
11C11×#388C211yesmaximal, characteristic
12C11×#387C211yesmaximal, characteristic, complemented
13C11×#385C211yesmaximal, characteristic
14C11×#385C211yesmaximal, characteristic
15C11×#384C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C11×#125—24no—
19C11×C22⋊Q8—24no—
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C4⋊C4C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27C2×C11×C4⋊C4C2211yescharacteristic
28C2×C11×C4⋊C4C2211yescharacteristic
29C2×C11×C4⋊C4C2211yescharacteristic
30C2×C11×C4⋊C4C2211yescharacteristic
31C2×C11×C4⋊C4C2211yescharacteristic
32C2×C11×C4⋊C4C2211yescharacteristic
33C2×C11×C4⋊C4C2211yescharacteristic
34C2×C11×C4⋊C4C2211yescharacteristic
35C2×C11×C22⋊C4C2211yescharacteristic
36C2×C11×C22⋊C4C2211yescharacteristic
37C2×C11×C22⋊C4C2211yescharacteristic
38C2×C11×C22⋊C4C2211yescharacteristic
39C2×C11×C22⋊C4C2211yescharacteristic
40C2×C11×C22⋊C4C2211yescharacteristic
41C2×C42×C11C2211yescharacteristic
42C2×C42×C11C2211yescharacteristic
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11×#95C2211yescharacteristic
46C11×#95C2211yescharacteristic
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11×#95C2211yescharacteristic
52C11×#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C2×Q8×C11—22no—
55C2×Q8×C11—41no—
56C2×Q8×C11—41no—
57C22×C4×C11—22no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C11×C4⋊C4—22no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4D414yes—
89C11×C22⋊C4—22no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4Q814yescomplemented
95C42×C11—22no—
96C42×C11—22no—
97#2720C1111yesmaximal, characteristic, direct product factor, Sylow
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11C2×Q812yes—
105C23×C11C2411yescharacteristic
106Q8×C11—44no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—44no—
144C2×C4×C11C2×D412yes—
145C2×C4×C11C2×D412yes—
146C2×C4×C11C2×D412yes—
147C2×C4×C11C2×Q812yes—
148C2×C4×C11C2×Q812yes—
149C2×C4×C11#4112yes—
150C2×#125C2×C1111yescharacteristic, complemented
151C2×C22⋊Q8C2×C1111yescharacteristic
152#400C2×C1111yescharacteristic, complemented
153#399C2×C1111yescharacteristic
154#398C2×C1111yescharacteristic, complemented
155#396C2×C1111yescharacteristic
156#395C2×C1111yescharacteristic, complemented
157#395C2×C1111yescharacteristic, complemented
158#389C2×C1111yescharacteristic, complemented
159#388C2×C1111yescharacteristic
160#388C2×C1111yescharacteristic
161#387C2×C1111yescharacteristic, complemented
162#385C2×C1111yescharacteristic
163#385C2×C1111yescharacteristic
164#384C2×C1111yescharacteristic, complemented
165C22×C11—22no—
166C22×C11—22no—
167C22×C11—22no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11C22×D411yescharacteristic
173C22×C11C22×Q811yescharacteristic
174C22×C11C2×#4111yescharacteristic
175C22×C11H(5,𝔽2)11yescharacteristic
176C22×C11H(5,𝔽2)11yescharacteristic
177C22×C112−1+411yescharacteristic
178C22×C112−1+411yescharacteristic
179C4×C11—22no—
180C4×C11—22no—
181C4×C11—22no—
182C4×C11—22no—
183C4×C11—22no—
184C4×C11—22no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—41no—
193C22×Q8C22×C1111yescharacteristic
194C23×C4C22×C1111yescharacteristic
195#125—24no—
196C22⋊Q8—24no—
197C2×C4⋊C4C22×C1111yescharacteristic
198C2×C4⋊C4C22×C1111yescharacteristic
199C2×C4⋊C4C22×C1111yescharacteristic
200C2×C4⋊C4C22×C1111yescharacteristic
201C2×C4⋊C4C22×C1111yescharacteristic
202C2×C4⋊C4C22×C1111yescharacteristic
203C2×C4⋊C4C22×C1111yescharacteristic
204C2×C4⋊C4C22×C1111yescharacteristic
205C2×C4⋊C4C22×C1111yescharacteristic
206C2×C4⋊C4C22×C1111yescharacteristic
207C2×C4⋊C4C22×C1111yescharacteristic
208C2×C4⋊C4C22×C1111yescharacteristic
209C2×C4⋊C4C22×C1111yescharacteristic
210C2×C4⋊C4C22×C1111yescharacteristic
211C2×C4⋊C4C22×C1111yescharacteristic
212C2×C22⋊C4C22×C1111yescharacteristic
213C2×C22⋊C4C22×C1111yescharacteristic
214C2×C22⋊C4C22×C1111yescharacteristic
215C2×C22⋊C4C22×C1111yescharacteristic
216C2×C22⋊C4C22×C1111yescharacteristic
217C2×C22⋊C4C22×C1111yescharacteristic
218C2×C42C22×C1111yescharacteristic
219C2×C42C22×C1111yescharacteristic
220#95C22×C1111yescharacteristic
221#95C22×C1111yescharacteristic
222#95C22×C1111yescharacteristic
223#95C22×C1111yescharacteristic
224#95C22×C1111yescharacteristic
225#95C22×C1111yescharacteristic
226#95C22×C1111yescharacteristic
227#95C22×C1111yescharacteristic
228#95C22×C1111yescharacteristic
229#95C22×C1111yescharacteristic
230C2×C11—42no—
231C2×C11#53511yescharacteristic
232C2×C11#53911yescharacteristic
233C2×C11#54411yescharacteristic
234C2×C11#54711yescharacteristic
235C2×C11D4×Q811yescharacteristic
236C2×C11#55411yescharacteristic
237C2×C11#56311yescharacteristic
238C24C23×C1111yescharacteristic
239C2×Q8—22no—
240C2×Q8—41no—
241C2×Q8—41no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4C23×C1111yescharacteristic
246C22×C4C23×C1111yescharacteristic
247C22×C4C23×C1111yescharacteristic
248C22×C4C23×C1111yescharacteristic
249C22×C4C23×C1111yescharacteristic
250C22×C4C23×C1111yescharacteristic
251C22×C4C23×C1111yescharacteristic
252C22×C4C23×C1111yescharacteristic
253C22×C4C23×C1111yescharacteristic
254C22×C4C23×C1111yescharacteristic
255C22×C4C23×C1111yescharacteristic
256C22×C4C23×C1111yescharacteristic
257C22×C4C23×C1111yescharacteristic
258C22×C4C23×C1111yescharacteristic
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4D4×C1114yes—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4Q8×C1114yescomplemented
280C42—22no—
281C42—22no—
282C11#272011yescharacteristic, direct product factor, Sylow
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23C2×Q8×C1112yes—
290C23C24×C1111yescharacteristic
291Q8—44no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—44no—
329C2×C4C2×D4×C1112yes—
330C2×C4C2×D4×C1112yes—
331C2×C4C2×D4×C1112yes—
332C2×C4C2×Q8×C1112yes—
333C2×C4C2×Q8×C1112yes—
334C2×C4C11×#4112yes—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22C22×D4×C1111yescharacteristic
343C22C22×Q8×C1111yescharacteristic
344C22C2×C11×#4111yescharacteristic
345C22C11×H(5,𝔽2)11yescharacteristic
346C22C11×H(5,𝔽2)11yescharacteristic
347C22C11×2−1+411yescharacteristic
348C22C11×2−1+411yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—41no—
363C2—42no—
364C2C11×#53511yescharacteristic
365C2C11×#53911yescharacteristic
366C2C11×#54411yescharacteristic
367C2C11×#54711yescharacteristic
368C2D4×Q8×C1111yescharacteristic
369C2C11×#55411yescharacteristic
370C2C11×#56311yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC24×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C11×#125C2semidirect
3. C11×#400C2semidirect
5. C11×#398C2semidirect
7. C11×#395C2semidirect
8. C11×#395C2semidirect
9. C11×#389C2semidirect
12. C11×#387C2semidirect
15. C11×#384C2semidirect
94. C11×C22⋊C4Q8semidirect
97. #2720C11direct (N × H)
150. C2×#125C2×C11semidirect
152. #400C2×C11semidirect
154. #398C2×C11semidirect
156. #395C2×C11semidirect
157. #395C2×C11semidirect
158. #389C2×C11semidirect
161. #387C2×C11semidirect
164. #384C2×C11semidirect
279. C22⋊C4Q8×C11semidirect
282. C11#2720direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C11×#1252
C2×C11×C22⋊Q82
C11×#4002
C11×#3992
C11×#3982
C11×#3962
C11×#3952
C11×#3892
C11×#3882
C11×#3872
C11×#3852
C11×#3842
#272011